Glasgow City Council will consider banning future Orange Order marches after footage showed members of the public chanting a sectarian song.
Footage emerged online of people appearing to sing the anti-Irish "Famine Song" at the weekend, while a band played along.
The council said the right of the Orange Order to march was not "absolute".
And it warned future parades could face greater restrictions or prohibition.
Police are investigating the footage of the song, which is sung to the tune of the Beach Boys' Sloop John B has previously been ruled to be racist by a Scottish court.
'Rights of others'
A spokesman for Glasgow City Council said: "The European Convention on Human Rights enshrines the rights to peaceful assembly and freedom of expression.
"However, these rights are not absolute. They must be balanced by the responsibility to ensure the rights of others are not infringed."
He added that the council would have a full debrief with police and the parade organisers, and would take into account any issues of public disorder, anti-social behaviour or damage to property resulting from the procession.
And the spokesman said the council would also "take into consideration any evidenced issues and, if a future procession notification is received from the organiser, the likelihood of any restriction or prohibition may be greater."
The main County Grand Orange Order parade from George Square to Glasgow Green on Saturday saw 4,500 people in 63 bands take part and another 4,000 people spectating.
It was in celebration of Prince William of Orange's victory over King James II at the Battle of the Boyne in 1690.
Eight arrests were made for minor disorder and alcohol-related offences.
Robert McLean, executive officer for the Grand Orange Lodge of Scotland, said: "At the end of the day, members of the public will sing songs to tunes.
"I have been quite clear - if police investigate we will assist with their inquiries. We look forward to the debrief and looking at any incidents that occurred."
But David Scott, campaign director for anti-sectarian group Nil by Mouth, said: "If the Orange Order are a religious and cultural organisation, what would be the relevance of a Beach Boys song?
"We know that tune also has another certain set of lyrics. The organisers should be speaking to band members and saying what is acceptable."
Ch Supt Brian McInulty of Police Scotland said the force operated a "zero-tolerance policy" when it comes to any form of sectarian abuse, and would fully investigate any incidents brought to their attention.